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Thermo-mechanical analysis of Wire and Arc Additive Layer Manufacturing process on large multi-layer parts
Computational Materials Science 50 (2011) 3315–3322
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Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
Thermo-mechanical analysis of Wire and Arc Additive Layer Manufacturing process on large multi-layer parts J. Ding a,⇑, P. Colegrove b, J. Mehnen a, S. Ganguly b, P.M. Sequeira Almeida b, F. Wang b, S. Williams b a b
Manufacturing Department, Cranfield University, Cranfield MK43 0AL, UK Welding Engineering Research Centre, Cranfield University, Cranfield MK43 0AL, UK
a r t i c l e
i n f o
Article history: Received 15 November 2010 Received in revised form 4 May 2011 Accepted 17 June 2011 Available online 12 July 2011 Keywords: Additive Layer Manufacturing Thermo-mechanical analysis Lagrangian model Eulerian model Residual stress Distortion
a b s t r a c t Wire and Arc Additive Layer Manufacturing (WAALM) is gaining increasing popularity as the process allows the production of large custom-made metal workpieces with high deposition rates. The high power input of the welding process, causes significant residual stress and distortion of the workpiece. This paper describes the thermo-mechanical behaviour of the multi-layer wall structure made by the WAALM process. A 3D thermo-elastic–plastic transient model and a model based on an advanced steady-state thermal analysis are employed in this study. This modelling approach shows a significant advantage with respect to the computational time. The temperature simulations and distortion predictions are verified by comparing with the experimental results from thermo-couples and laser scanners, while the residual stresses are verified with the neutron diffraction strain scanner ENGIN-X. The stress across the deposited wall is found uniform with very little influence of the preceding layers on the following layers. The stress redistributed after unclamping with a much lower value at the top of the wall than at the interface due to the bending distortion of the sample. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction Additive Layer Manufacturing has become an important industrial process for the manufacture of custom-made metal workpieces. Innovative Wire and Arc Additive Layer Manufacture (WAALM) solutions have emerged recently to fabricate highly reactive metallic components in an out-of-chamber environment (e.g. Ti–6Al–4V) [1]. Faster processing speeds and high deposition rate capabilities are central attributes to enable the production of large-scale aerospace components [2]. Although the wire-added ALM process has been around for almost a century – the first patent was filed 1920 by Baker [3] – modern welding and automation technologies provide opportunities that were not previously available. In addition, there is currently a demand for sustainable, low cost, environmentally friendly processes with high geometric flexibility. Finally, WAALM can be used to deposit a variety of materials that can be welded, such as steel [4,5], Ni alloys [6], and Ti alloys [1,7]. In the WAALM process, 3D metallic components are built by depositing beads of weld metal in a layer by layer fashion. Standard wire based welding processes such as Gas Metal Arc Welding (GMAW) and Gas Tungsten Arc Welding (GTAW) are low cost solutions employed as heat sources, providing high deposition rates by utilising high energy input. ⇑ Corresponding author. E-mail address: jialuo.ding@cranfield.ac.uk (J. Ding). 0927-0256/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.commatsci.2011.06.023
However, the high heat input leads to significant distortion and residual stress. Finite Element (FE) analysis can be used to predict the residual stress and distortion during additive manufacturing processes [8–10], enabling the development of mitigation methods [11,12]. Most of the FE analyses utilise transient models with a moving heat source. Element birth technique is used for simulating addition of material, providing accurate predictions. However, the model size is usually limited due to the computational time required for these simulations due to the long processing time to make the real parts. Therefore to develop models of large-scale WAALM components, which can scale to several metres, the conventional transient FE analysis is not suitable. A new method is needed to reduce the calculation time while keeping the simulation accuracy high. For a long weld with a constant welding speed, the thermal histories approach a steady state, particularly in the middle of the weld. This phenomenon has been utilised in FE models of welding processes which have used a steady state model [13–16,18]. Unlike the conventional transient method which uses a time increment scheme to model the moving welding torch, the steady state method attaches an Eulerian reference frame to the welding torch and the material ‘‘flows’’ through the mesh (Fig. 1). Therefore the problem can be solved for a single time step saving a large amount of computational time. Moreover, the model using the Eulerian frame does not need to use a high density mesh uniformly along the weld line, saving additional computational time [14]. While the steady state solution of the thermal problem is relatively
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trivial, application to the mechanical problem is more difficult, but has been demonstrated by several authors [13,14,16,17]. An alternative approach, developed by Colegrove et al. [18] cut the Eulerian thermal model into a series of temperature data slices, and then transferred the sliced temperature data onto a 2D elastic–plastic model.
In this paper, an efficient FE method is developed to analyse the thermo-mechanical performance of the WAALM process on a 500 mm mild steel multi-layer wall structure. Steady state temperature distributions are calculated using the Eulerian thermal method, which are used as an input to a 3D mechanical model for residual stress and distortion analysis. A comparison was carried out between this efficient FE model and a conventional transient thermo-mechanical model. Both models are compared with experimental measurements of temperature, residual stress and distortion. 2. Experimental method
Fig. 1. Model with different reference frames. (a) Lagrangian reference frame. (b) Eulerian reference frame.
Sample walls were produced in mild steel using WAALM. The base plates used in the experiments were rolled structural steel plates (grade S355JR-AR). The chemical composition of the alloy (in wt.%) is 0.24% C, 1.60% Mn, 0.55% Si, 0.045% P, 0.045% S, 0.009% N, 0.003–0.100% Nb and Fe balance. The selection of the consumable electrode was based on a strict chemical composition criterion in order to obtain optimum as welded mechanical properties. The chemical composition of the solid wire (in wt.%) is 0.08% C, 1.50% Mn, 0.92% Si, 0.16% Cu, 60.040% P, 60.035% S and Fe balance. The geometry of the structure with a four layer wall is shown in Fig. 2a. The walls were deposited along the centreline of the base plate with an approximate width of 5 mm and height of 2 mm
Fig. 2. Geometry of the WAALM samples: (a) four layer specimen and (b) cross-section of the 20 layer specimen. Note that the location of the residual stress measurements are shown by the red dashed line. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Fig. 3. Mesh of transient thermal model.
for each layer. The heat source is a Cold Metal Transfer (CMT) [23] welding power source, a modified GMAW variant based on controlled dip transfer mode mechanism, which can provide a high deposition rate capability with relatively low heat input. The welding wire used in this study is 1.2 mm and the wire feed speed is 10 m min1. The travel speed of the welding torch is 8.33 mm s1. The welding process heat input is 269.5 J mm1, assuming an efficiency of 0.9. A water cooled aluminium backing plate was utilised in order to cool the sample more rapidly. A waiting time of 400 s was used between subsequent layers enabling the sample to cool below 50 °C before new layers were deposited. Four k-type thermocouples were welded at the positions indicated in Fig. 2a. The experimental trial involved the production of five specimens and involved the deposition of one, two, three, four and twenty layers. The last involved depositing a 20 layer wall. The four layer specimen is shown in Fig. 2a, and the 20 layer specimen is shown in Fig. 2b. To verify the mechanical model, residual strain measurements were carried out at the ENGIN-X strain scanner at ISIS, Oxford, UK. Strain measurements were taken in the base plate 2 mm below the top surface along a line transverse to the weld direction which is shown in section B-B of Fig. 2a. This was done for the one, two and three layer specimens. Strains in three directions were also measured along the wall for the 20 layer specimen, as shown in Fig. 2b. The time-of-flight principle of strain measurement is utilised to determine the lattice strain [24,25]. The longitudinal strain direction was measured using a gauge volume of 2 2 2 mm3, while the transverse and normal strain directions were measured using a gauge volume of 2 20 2 mm3. The opening of the vertical dimension of the incoming beam during measurement of the transverse and normal strain directions would lead to a faster measurement with higher neutron flux without the loss of any spatial resolution. The data analysis was performed for a time-of-flight spectrum of 20–40 ms which contains the {1 1 0}, {2 0 0} and {2 1 1} families of crystallographic planes. The range and families of crystallographic planes analysed ensured an average macroscopic strain determination free from crystal anisotropy. The diffraction spectrum was analysed by Pawley refinement [26] using GSAS software. References for strain calculations were measured in the far field parent in a 3 mm thick slice removed from the edge of the specimens. A constant stress free value was used for the calculations of the strain in the base plate because the penetration level of the deposited wire did not affect the composition of the measurement location in the base plate. A reference slice which
included the whole deposited wall was used for the measurements on the 20 layer wall. Strain measured in all the three directions were then combined to analyse the stress assuming the measured directions are the principal strain directions and following Hooke’s law as
rx ¼
E Et ex þ ðex þ ey þ ez Þ ð1 þ tÞ ð1 þ tÞð1 2tÞ
ð1Þ
where ex, ey and ez are the strains in the principal directions; E is the elasticity of the material; and t is Poisson’s ratio of the material.In addition, distortion was taken from the sample with four layer wall using a Romer Omega Arm with R-Scan 3D laser scanning system.
3. Thermo-mechanical FEM models 3.1. FE thermal models The FE software package, ABAQUS [19] was used for both the thermal and mechanical models. Sequentially coupled thermo-mechanical simulations were carried out which calculated the temperature distribution first and then used the results for the mechanical analysis. Two model types were developed for the thermo-mechanical simulation of a four layer wall. The first used a steady state thermal model which used an Eulerian reference frame, and the second used a transient model and Lagrangian reference frame. Only half of the material is modelled due to the symmetry along the central axis which shown as A–A in Fig. 2a. For the Lagrangian thermal model, linear brick elements with eight nodes (DC3D8) are used for the thermal simulation. To capture the thermal performance around the heat source, dense meshes of size 2 mm 0.833 mm 0.667 mm were used for the bead and the area near the welding line. The meshes became coarser in the y direction and z direction away from the welding line (Fig. 3). The filler material was simulated using the ‘‘element birth technique’’ [21]. All the elements of the bead are deactivated at the first step of the analysis, and then the elements are activated sequentially following the heat source.
Table 1 Heat source parameters. af (mm)
ar (mm)
b (mm)
c (mm)
Q (W)
ff
fr
2
6
2.5
3
2245.83
0.6
1.4
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Fig. 4. Mesh of the steady state thermal model.
The moving heat source for the Lagrangian thermal model is generated with the user subroutine DFLUX in the ABAQUS code. The Goldak double ellipsoidal heat source [20] was used to apply the heat to the additive manufacture deposits. The power density of the region in front of the arc centre and the region behind the arc centre is defined separately using:
pffiffiffi 2 2 2 3 x2 þy2 þz2 6 3Qff c a b f e qf ¼ pffiffiffiffi p paf bc h i pffiffiffi 2 y2 2 3 x2 þ 2 þz2 6 3Qfr c a b r qr ¼ pffiffiffiffi e p par bc ff þ fr ¼ 2
ð2Þ
where af and ar are the length of the frontal ellipsoid and the rear ellipsoid, respectively; b is the width of the heat source; c is the depth of the heat source; Q is the energy input considering the factor of efficiency; ff and fr are the factors for distributing the power to the front and rear of the hear source. The parameters used for the heat source model are shown in Table 1. Table 2 Computational time comparison between the transient model and the steady state based model.
Transient model Steady state model Time saving
Thermal analysis time
Mechanical analysis time
Total analysis time
51 h, 24 min 10 min 99.69%
24 h, 1 min 14 h, 46 min 38.51%
75 h, 25 min 14 h, 56 min 80.21%
Fig. 4 shows the mesh used for the steady-state model. Unlike the transient model, the steady-state model does not require a uniform mesh with high density along the weld line. Forced convection/diffusion brick elements (DCC3D8) were utilised in this model. The smallest elements are located in the heating area with a size of 1.7 mm 0.83 mm 0.67 mm, while the largest ones are at the outlet face with a size of 345 mm 5.4 mm 2.7 mm. A mass flow rate per area, which equals to the welding speed multiplied by the material density, is used to represent the torch movement. The heat distribution for the steady state model is also represented with the same Goldak double ellipsoidal heat source. As the component did not cool down to ambient temperature between deposits it was necessary to include the effect of the residual temperature in the models for the newly added layers. This was done by taking the nodal temperatures from the outlet surface for the previous model and applying them to the inlet surface of the model for the next layer. To provide an accurate prediction of the outlet temperature the length of the model is set so that:
L ¼ V torch T waiting þ Lactual
ð3Þ
where L is the length of the Eulerian thermal model; Vtorch is the travel speed of the welding torch; Twaiting is the waiting time between subsequent layers; and Lactual is the actual length of the sample. Using this approach, the effective cooling time between subsequent layers is identical to the experimental condition. Both models used thermal material properties from Zhang and Michaleris [16]. An artificially high thermal conductivity is used for temperatures greater than 1500 °C to capture the convective heat transfer in the weld pool. The radiation coefficient and
Fig. 5. Temperature distribution from: (a) transient and (b) steady-state thermal models.
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the convection coefficient are assumed independent of the temperature and are set to 0.2 and 5.7 Wm2K1, respectively. The heat loss through the cooling system under the base plate is modelled with an equivalent convection coefficient. This coefficient was found by running a series of numerical trials, and tuning the value so that the predicted temperature profiles matched the experimental results. A value of 300 Wm2K1 gave the best match with the experiments.
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ing one step with transient mechanical model is 32 increments on average, while the mechanical model using the mapped steady state thermal results needs only 20 increments to complete the same step. Thus, the time taken for the mechanical model based on the steady-state model was reduced by around 40%. Hence the total time saving with the new model is around 80%.
3.2. FE mechanical models The Lagrangian mechanical model uses the same meshing as the Lagrangian thermal model, but the mesh type is changed to integrated 3D 8-node element (C3D8R). The steps for the mechanical simulation are set with the same number and time as the thermal simulation. The nodal temperature results calculated from the thermal analysis are utilised as thermal load input for the mechanical simulation. A 3D elastic–plastic mechanical model is used to calculate the residual stress from the steady state thermal model data. The length of the mechanical model was 500 mm which was the actual length of the experimental sample. It was meshed with the same mesh spacing as the steady state model in the y and z directions, however the spacing in the x direction was set to a constant value of 2.5 mm. To use the steady state thermal results as the input to the mechanical model, the static nodal temperature data were transferred to thermal histories by dividing the position in the x direction by the travel speed. Temperature histories were added sequentially using the results from the model with one layer bead to the model with four layer bead. The stress analysis was carried out by applying the transferred thermal history sequentially to the 3D mechanical model. The temperature field from the steady state model is effectively mapped to the mechanical model using a preprocessing programme generated in Matlab. ‘‘Element birth technique’’ was utilised in both mechanical models for simulating the addition of each layer. Both models used temperature dependant mechanical properties from Zhang and Michaleris [16]. The phase transformations are ignored in this study, as it has an insignificant effect on the welding residual stress for mild steel [22]. To avoid difficulties in convergence, a ‘cut-off temperature’ of 1000 °C was used in the material model. The Young’s modulus and the yield stress of the material remain at the same value for temperatures above the cut off temperature. To simulate the clamping system used in the WAALM process, a ‘backing plate’ was included with rigid material properties. A hard contact is applied between the contact surface of the base plate and the backing plate. This prevents the points on the base plate moving in z direction but not against the movement in +z direction. Clamps in the real WAALM experiment are located on the four corners and the mid length of the base plate. This was modelled by fixing the movements of the nodes at the corresponding positions. The clamping constraints were removed in the stages when the base plate was unclamped. 3.3. Time comparison The comparison of the computational time used for the two models is presented in Table 2. All the simulations were calculated on a grid computing system with four processors. The computational time consumed by the transient thermal model can be greatly reduced by using the steady-state model. The transient thermal model provides much more data than the steady state model as it calculates the incremental temperature histories, which result in more time increments needed for completing the mechanical analysis. The number of time increments for complet-
Fig. 6. Temperature verification on the measuring positions of (a) TP1 (250, 5, 0), (b) TP2 (250, 20, 0), (c) TP3 (250, 0, 12), and (d) TP4 (375, 0, 8).
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4. Results and discussion 4.1. Thermal results Fig. 5 presents the contour plots of temperature results of the Lagrangian thermal model and the Eulerian thermal model, respectively. Both models produced similar heating and cooling cycles. The thermal models were verified by comparing the temperature history results from the four thermocouples positions on the base plate shown in Fig. 2a. These results are presented in Fig. 6 for the four layer specimen. As the steady-state model does not have a time related history, the thermal cycle of the testing point is obtained by plotting the temperature along lines with fixed y, and z coordinates which correspond to the thermocouple positions shown in Fig. 2a. The time coordinate is found by dividing the position in the x direction by the travel speed. Both, the transient and steady-state thermal models give accurate predictions of the temperatures at the four thermocouple positions. Although the steady state model underestimates the temperature marginally because heat can be conducted via the elements behind the heat source, the effect is small because of the high travel speed. 4.2. Mechanical results Fig. 7a and b illustrates the predicted longitudinal residual stress of the four layer wall with clamping from the two model types, which indicate similar results. The heat from the welding process causes a tensile residual stress along the weld bead due to material contraction during solidification, which causes a balancing compressive residual stress in the base plate. Note that the magnitude of the compressive stress is greatest where clamping has been applied due to the restraint in this region. There is sig-
nificant distortion of the component and relaxation of the stresses after the clamping was removed which is illustrated in Fig. 7c. To better understand these stress changes, the longitudinal stress was plotted along the dotted lines in Fig. 7b and c in Fig. 7d. Fig. 7d shows that when the specimen is clamped, the highest longitudinal stress occurs in the deposited wall. The stress predicted across the deposit is very uniform with very little annealing of the earlier layers by the latter ones. To further investigate this finding, a further four layers were deposited (giving eight layers in total) and the results plotted in Fig. 7d. There is little change in the stresses generated, further supporting this finding. Indeed Chin et al. [8] found a similar result in their model of additive layer manufacture. The stresses in the base plate adjacent to the deposited wall are also tensile, however there is a significant drop in magnitude since the material in the base is softer than the weld metal. Note that in the model there is a distinct jump in material properties at the interface which does occur in practice due to dilution effects. It is only near the bottom of the base plate that the longitudinal stresses go into compression. The significant drop in the longitudinal stress after unclamping is also shown in Fig. 7d. The interesting aspects of this plot occur toward the extremities. For example, the stress at the top of the deposited wall has a much lower value than at the interface due to the bending distortion of the sample. This distortion also causes the compressive stress at the bottom of the base plate to go into tension. There is a small reduction in the tensile longitudinal residual stress measured in the base plate with increased layers due to the influence of bending distortion. This is reflected in the residual stress measurements shown in Fig. 7d where four and eight layer walls are compared unclamped. To have an overall check of the mechanical results from the model, the predicted distortion along the long edge from the two mechanical models was compared with the measured distortion
Fig. 7. Longitudinal residual stress predictions from: (a) transient thermal and mechanical models, (b) steady state thermal and mapped mechanical models, (c) steady state thermal and mapped mechanical models after clamps were removed (a scaling factor of 5 is used for the distorted shape), and (d) the stress plotted along the lines shown in of (b and c).
J. Ding et al. / Computational Materials Science 50 (2011) 3315–3322
Fig. 8. Distortion verification along the longitudinal direction after the clamps were removed.
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Fig. 10. Longitudinal stress along the normal direction of the mid-section in the deposited wall.
from the two long edges of the sample. Fig. 8 shows how the distorted shape from both models is nearly identical and agrees with the experimentally measured distortion. Detailed validation of the residual stress data was provided by comparing the computational results from the one, two and three layer specimens with those from neutron diffraction measurements. Fig. 9 shows the comparison on the base plate. In both the modelling and experimental results the clamps have been removed, and three principle directions have been considered namely: longitudinal (r LD), transverse (r TD), and normal (r ND). The results are similar to those observed in long welding processes with the longitudinal stress dominating over the transverse and normal stresses [21]. The FE predictions match the experimental results well in all cases except the one layer wall where the model underpredicts the stresses. Moreover, there is a more significant reduction in the experimentally measured stresses between the 1 and 2 layer walls, than in the stresses predicted by the models. A possible explanation is that the model does not fully capture the microstructural changes which occur in the actual material. The comparison between the measured residual stresses from a 20 layer specimen with those from the model is shown in Fig. 10. In both the model and experiments the specimen is unclamped, and the comparison is along the centreline of the deposit as shown in Fig. 2b. A sample with a 20 layer wall was made to validate the residual stress on the deposited wall. Longitudinal stress was measured without clamps in the mid-section along the normal direction of the deposited wall. Due to the long computational time the transient model needed, the model based on the steady-state thermal solution was used for the prediction. The comparison shows that the numerical prediction matches the experimental result well and the overall shape is similar to that observed for the four and eight layer specimens in Fig. 7d. In general, unevenly distributed stresses generated during the WAALM process can cause large distortion of the parts after clamp removal. Depending on the application, it will be necessary to provide a subsequent heat treatment to relieve these stresses and improve the mechanical properties that would otherwise be negatively affected. The FEM models introduced in this paper can provide accurate prediction of the stresses and distortions of the WAALM process. This will be useful for future work where the WAALM process will be optimised to minimise the residual stress and distortion. 5. Conclusions Fig. 9. Stresses in the longitudinal (LD), transverse (TD) and normal (ND) directions along a transverse line in the base-plate indicated in Fig. 2a for (a) single, (b) two, and (c) three layers.
In this study, the thermo-elastic–plastic FEM is employed to simulate the thermo-mechanical performance of large multi-layer
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wall shaped WAALM structures. Experiments are carried out to verify the temperature distribution, stress distribution and distortions. Moreover, an efficient FE method based on Eulerian steadystate thermal analysis is also discussed. According to the results in this study, the following conclusions can be drawn: (1) Both FEM models can accurately predict the heating and cooling cycles during the WAALM process. The steady-state model can also be used for dealing with the multi-layer WAALM process. (2) The stress evolution analysed using the numerical model shows that stress across the deposit is very uniform with very little influence of the preceding layers on the following layers. (3) A significant stress redistribution is observed after unclamping. The stress at the top of the deposited wall has a much lower value than at the interface due to the bending distortion of the sample. The neutron diffraction strain scanner ENGIN-X reveals a good match of the predicted stress data with the measurements. The measured distortions also support the model predictions. (4) The new FEM approach based on the steady-state thermal model shows a significant advantage of around 80% on the computational time. This will be useful for future work where the WAALM process will be optimised to minimise the residual stress and distortion.
Acknowledgements This research was carried out under RUAM project (131) of the IMRC (Innovative Manufacturing Research Centre) Cranfield funded by EPSRC, UK. The authors would like to thank Flemming Nielsen for his technical assistance and Dr. Anna Paradowska for her support in ISIS.
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Contents lists available at ScienceDirect
Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
Thermo-mechanical analysis of Wire and Arc Additive Layer Manufacturing process on large multi-layer parts J. Ding a,⇑, P. Colegrove b, J. Mehnen a, S. Ganguly b, P.M. Sequeira Almeida b, F. Wang b, S. Williams b a b
Manufacturing Department, Cranfield University, Cranfield MK43 0AL, UK Welding Engineering Research Centre, Cranfield University, Cranfield MK43 0AL, UK
a r t i c l e
i n f o
Article history: Received 15 November 2010 Received in revised form 4 May 2011 Accepted 17 June 2011 Available online 12 July 2011 Keywords: Additive Layer Manufacturing Thermo-mechanical analysis Lagrangian model Eulerian model Residual stress Distortion
a b s t r a c t Wire and Arc Additive Layer Manufacturing (WAALM) is gaining increasing popularity as the process allows the production of large custom-made metal workpieces with high deposition rates. The high power input of the welding process, causes significant residual stress and distortion of the workpiece. This paper describes the thermo-mechanical behaviour of the multi-layer wall structure made by the WAALM process. A 3D thermo-elastic–plastic transient model and a model based on an advanced steady-state thermal analysis are employed in this study. This modelling approach shows a significant advantage with respect to the computational time. The temperature simulations and distortion predictions are verified by comparing with the experimental results from thermo-couples and laser scanners, while the residual stresses are verified with the neutron diffraction strain scanner ENGIN-X. The stress across the deposited wall is found uniform with very little influence of the preceding layers on the following layers. The stress redistributed after unclamping with a much lower value at the top of the wall than at the interface due to the bending distortion of the sample. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction Additive Layer Manufacturing has become an important industrial process for the manufacture of custom-made metal workpieces. Innovative Wire and Arc Additive Layer Manufacture (WAALM) solutions have emerged recently to fabricate highly reactive metallic components in an out-of-chamber environment (e.g. Ti–6Al–4V) [1]. Faster processing speeds and high deposition rate capabilities are central attributes to enable the production of large-scale aerospace components [2]. Although the wire-added ALM process has been around for almost a century – the first patent was filed 1920 by Baker [3] – modern welding and automation technologies provide opportunities that were not previously available. In addition, there is currently a demand for sustainable, low cost, environmentally friendly processes with high geometric flexibility. Finally, WAALM can be used to deposit a variety of materials that can be welded, such as steel [4,5], Ni alloys [6], and Ti alloys [1,7]. In the WAALM process, 3D metallic components are built by depositing beads of weld metal in a layer by layer fashion. Standard wire based welding processes such as Gas Metal Arc Welding (GMAW) and Gas Tungsten Arc Welding (GTAW) are low cost solutions employed as heat sources, providing high deposition rates by utilising high energy input. ⇑ Corresponding author. E-mail address: jialuo.ding@cranfield.ac.uk (J. Ding). 0927-0256/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.commatsci.2011.06.023
However, the high heat input leads to significant distortion and residual stress. Finite Element (FE) analysis can be used to predict the residual stress and distortion during additive manufacturing processes [8–10], enabling the development of mitigation methods [11,12]. Most of the FE analyses utilise transient models with a moving heat source. Element birth technique is used for simulating addition of material, providing accurate predictions. However, the model size is usually limited due to the computational time required for these simulations due to the long processing time to make the real parts. Therefore to develop models of large-scale WAALM components, which can scale to several metres, the conventional transient FE analysis is not suitable. A new method is needed to reduce the calculation time while keeping the simulation accuracy high. For a long weld with a constant welding speed, the thermal histories approach a steady state, particularly in the middle of the weld. This phenomenon has been utilised in FE models of welding processes which have used a steady state model [13–16,18]. Unlike the conventional transient method which uses a time increment scheme to model the moving welding torch, the steady state method attaches an Eulerian reference frame to the welding torch and the material ‘‘flows’’ through the mesh (Fig. 1). Therefore the problem can be solved for a single time step saving a large amount of computational time. Moreover, the model using the Eulerian frame does not need to use a high density mesh uniformly along the weld line, saving additional computational time [14]. While the steady state solution of the thermal problem is relatively
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trivial, application to the mechanical problem is more difficult, but has been demonstrated by several authors [13,14,16,17]. An alternative approach, developed by Colegrove et al. [18] cut the Eulerian thermal model into a series of temperature data slices, and then transferred the sliced temperature data onto a 2D elastic–plastic model.
In this paper, an efficient FE method is developed to analyse the thermo-mechanical performance of the WAALM process on a 500 mm mild steel multi-layer wall structure. Steady state temperature distributions are calculated using the Eulerian thermal method, which are used as an input to a 3D mechanical model for residual stress and distortion analysis. A comparison was carried out between this efficient FE model and a conventional transient thermo-mechanical model. Both models are compared with experimental measurements of temperature, residual stress and distortion. 2. Experimental method
Fig. 1. Model with different reference frames. (a) Lagrangian reference frame. (b) Eulerian reference frame.
Sample walls were produced in mild steel using WAALM. The base plates used in the experiments were rolled structural steel plates (grade S355JR-AR). The chemical composition of the alloy (in wt.%) is 0.24% C, 1.60% Mn, 0.55% Si, 0.045% P, 0.045% S, 0.009% N, 0.003–0.100% Nb and Fe balance. The selection of the consumable electrode was based on a strict chemical composition criterion in order to obtain optimum as welded mechanical properties. The chemical composition of the solid wire (in wt.%) is 0.08% C, 1.50% Mn, 0.92% Si, 0.16% Cu, 60.040% P, 60.035% S and Fe balance. The geometry of the structure with a four layer wall is shown in Fig. 2a. The walls were deposited along the centreline of the base plate with an approximate width of 5 mm and height of 2 mm
Fig. 2. Geometry of the WAALM samples: (a) four layer specimen and (b) cross-section of the 20 layer specimen. Note that the location of the residual stress measurements are shown by the red dashed line. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Fig. 3. Mesh of transient thermal model.
for each layer. The heat source is a Cold Metal Transfer (CMT) [23] welding power source, a modified GMAW variant based on controlled dip transfer mode mechanism, which can provide a high deposition rate capability with relatively low heat input. The welding wire used in this study is 1.2 mm and the wire feed speed is 10 m min1. The travel speed of the welding torch is 8.33 mm s1. The welding process heat input is 269.5 J mm1, assuming an efficiency of 0.9. A water cooled aluminium backing plate was utilised in order to cool the sample more rapidly. A waiting time of 400 s was used between subsequent layers enabling the sample to cool below 50 °C before new layers were deposited. Four k-type thermocouples were welded at the positions indicated in Fig. 2a. The experimental trial involved the production of five specimens and involved the deposition of one, two, three, four and twenty layers. The last involved depositing a 20 layer wall. The four layer specimen is shown in Fig. 2a, and the 20 layer specimen is shown in Fig. 2b. To verify the mechanical model, residual strain measurements were carried out at the ENGIN-X strain scanner at ISIS, Oxford, UK. Strain measurements were taken in the base plate 2 mm below the top surface along a line transverse to the weld direction which is shown in section B-B of Fig. 2a. This was done for the one, two and three layer specimens. Strains in three directions were also measured along the wall for the 20 layer specimen, as shown in Fig. 2b. The time-of-flight principle of strain measurement is utilised to determine the lattice strain [24,25]. The longitudinal strain direction was measured using a gauge volume of 2 2 2 mm3, while the transverse and normal strain directions were measured using a gauge volume of 2 20 2 mm3. The opening of the vertical dimension of the incoming beam during measurement of the transverse and normal strain directions would lead to a faster measurement with higher neutron flux without the loss of any spatial resolution. The data analysis was performed for a time-of-flight spectrum of 20–40 ms which contains the {1 1 0}, {2 0 0} and {2 1 1} families of crystallographic planes. The range and families of crystallographic planes analysed ensured an average macroscopic strain determination free from crystal anisotropy. The diffraction spectrum was analysed by Pawley refinement [26] using GSAS software. References for strain calculations were measured in the far field parent in a 3 mm thick slice removed from the edge of the specimens. A constant stress free value was used for the calculations of the strain in the base plate because the penetration level of the deposited wire did not affect the composition of the measurement location in the base plate. A reference slice which
included the whole deposited wall was used for the measurements on the 20 layer wall. Strain measured in all the three directions were then combined to analyse the stress assuming the measured directions are the principal strain directions and following Hooke’s law as
rx ¼
E Et ex þ ðex þ ey þ ez Þ ð1 þ tÞ ð1 þ tÞð1 2tÞ
ð1Þ
where ex, ey and ez are the strains in the principal directions; E is the elasticity of the material; and t is Poisson’s ratio of the material.In addition, distortion was taken from the sample with four layer wall using a Romer Omega Arm with R-Scan 3D laser scanning system.
3. Thermo-mechanical FEM models 3.1. FE thermal models The FE software package, ABAQUS [19] was used for both the thermal and mechanical models. Sequentially coupled thermo-mechanical simulations were carried out which calculated the temperature distribution first and then used the results for the mechanical analysis. Two model types were developed for the thermo-mechanical simulation of a four layer wall. The first used a steady state thermal model which used an Eulerian reference frame, and the second used a transient model and Lagrangian reference frame. Only half of the material is modelled due to the symmetry along the central axis which shown as A–A in Fig. 2a. For the Lagrangian thermal model, linear brick elements with eight nodes (DC3D8) are used for the thermal simulation. To capture the thermal performance around the heat source, dense meshes of size 2 mm 0.833 mm 0.667 mm were used for the bead and the area near the welding line. The meshes became coarser in the y direction and z direction away from the welding line (Fig. 3). The filler material was simulated using the ‘‘element birth technique’’ [21]. All the elements of the bead are deactivated at the first step of the analysis, and then the elements are activated sequentially following the heat source.
Table 1 Heat source parameters. af (mm)
ar (mm)
b (mm)
c (mm)
Q (W)
ff
fr
2
6
2.5
3
2245.83
0.6
1.4
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Fig. 4. Mesh of the steady state thermal model.
The moving heat source for the Lagrangian thermal model is generated with the user subroutine DFLUX in the ABAQUS code. The Goldak double ellipsoidal heat source [20] was used to apply the heat to the additive manufacture deposits. The power density of the region in front of the arc centre and the region behind the arc centre is defined separately using:
pffiffiffi 2 2 2 3 x2 þy2 þz2 6 3Qff c a b f e qf ¼ pffiffiffiffi p paf bc h i pffiffiffi 2 y2 2 3 x2 þ 2 þz2 6 3Qfr c a b r qr ¼ pffiffiffiffi e p par bc ff þ fr ¼ 2
ð2Þ
where af and ar are the length of the frontal ellipsoid and the rear ellipsoid, respectively; b is the width of the heat source; c is the depth of the heat source; Q is the energy input considering the factor of efficiency; ff and fr are the factors for distributing the power to the front and rear of the hear source. The parameters used for the heat source model are shown in Table 1. Table 2 Computational time comparison between the transient model and the steady state based model.
Transient model Steady state model Time saving
Thermal analysis time
Mechanical analysis time
Total analysis time
51 h, 24 min 10 min 99.69%
24 h, 1 min 14 h, 46 min 38.51%
75 h, 25 min 14 h, 56 min 80.21%
Fig. 4 shows the mesh used for the steady-state model. Unlike the transient model, the steady-state model does not require a uniform mesh with high density along the weld line. Forced convection/diffusion brick elements (DCC3D8) were utilised in this model. The smallest elements are located in the heating area with a size of 1.7 mm 0.83 mm 0.67 mm, while the largest ones are at the outlet face with a size of 345 mm 5.4 mm 2.7 mm. A mass flow rate per area, which equals to the welding speed multiplied by the material density, is used to represent the torch movement. The heat distribution for the steady state model is also represented with the same Goldak double ellipsoidal heat source. As the component did not cool down to ambient temperature between deposits it was necessary to include the effect of the residual temperature in the models for the newly added layers. This was done by taking the nodal temperatures from the outlet surface for the previous model and applying them to the inlet surface of the model for the next layer. To provide an accurate prediction of the outlet temperature the length of the model is set so that:
L ¼ V torch T waiting þ Lactual
ð3Þ
where L is the length of the Eulerian thermal model; Vtorch is the travel speed of the welding torch; Twaiting is the waiting time between subsequent layers; and Lactual is the actual length of the sample. Using this approach, the effective cooling time between subsequent layers is identical to the experimental condition. Both models used thermal material properties from Zhang and Michaleris [16]. An artificially high thermal conductivity is used for temperatures greater than 1500 °C to capture the convective heat transfer in the weld pool. The radiation coefficient and
Fig. 5. Temperature distribution from: (a) transient and (b) steady-state thermal models.
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the convection coefficient are assumed independent of the temperature and are set to 0.2 and 5.7 Wm2K1, respectively. The heat loss through the cooling system under the base plate is modelled with an equivalent convection coefficient. This coefficient was found by running a series of numerical trials, and tuning the value so that the predicted temperature profiles matched the experimental results. A value of 300 Wm2K1 gave the best match with the experiments.
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ing one step with transient mechanical model is 32 increments on average, while the mechanical model using the mapped steady state thermal results needs only 20 increments to complete the same step. Thus, the time taken for the mechanical model based on the steady-state model was reduced by around 40%. Hence the total time saving with the new model is around 80%.
3.2. FE mechanical models The Lagrangian mechanical model uses the same meshing as the Lagrangian thermal model, but the mesh type is changed to integrated 3D 8-node element (C3D8R). The steps for the mechanical simulation are set with the same number and time as the thermal simulation. The nodal temperature results calculated from the thermal analysis are utilised as thermal load input for the mechanical simulation. A 3D elastic–plastic mechanical model is used to calculate the residual stress from the steady state thermal model data. The length of the mechanical model was 500 mm which was the actual length of the experimental sample. It was meshed with the same mesh spacing as the steady state model in the y and z directions, however the spacing in the x direction was set to a constant value of 2.5 mm. To use the steady state thermal results as the input to the mechanical model, the static nodal temperature data were transferred to thermal histories by dividing the position in the x direction by the travel speed. Temperature histories were added sequentially using the results from the model with one layer bead to the model with four layer bead. The stress analysis was carried out by applying the transferred thermal history sequentially to the 3D mechanical model. The temperature field from the steady state model is effectively mapped to the mechanical model using a preprocessing programme generated in Matlab. ‘‘Element birth technique’’ was utilised in both mechanical models for simulating the addition of each layer. Both models used temperature dependant mechanical properties from Zhang and Michaleris [16]. The phase transformations are ignored in this study, as it has an insignificant effect on the welding residual stress for mild steel [22]. To avoid difficulties in convergence, a ‘cut-off temperature’ of 1000 °C was used in the material model. The Young’s modulus and the yield stress of the material remain at the same value for temperatures above the cut off temperature. To simulate the clamping system used in the WAALM process, a ‘backing plate’ was included with rigid material properties. A hard contact is applied between the contact surface of the base plate and the backing plate. This prevents the points on the base plate moving in z direction but not against the movement in +z direction. Clamps in the real WAALM experiment are located on the four corners and the mid length of the base plate. This was modelled by fixing the movements of the nodes at the corresponding positions. The clamping constraints were removed in the stages when the base plate was unclamped. 3.3. Time comparison The comparison of the computational time used for the two models is presented in Table 2. All the simulations were calculated on a grid computing system with four processors. The computational time consumed by the transient thermal model can be greatly reduced by using the steady-state model. The transient thermal model provides much more data than the steady state model as it calculates the incremental temperature histories, which result in more time increments needed for completing the mechanical analysis. The number of time increments for complet-
Fig. 6. Temperature verification on the measuring positions of (a) TP1 (250, 5, 0), (b) TP2 (250, 20, 0), (c) TP3 (250, 0, 12), and (d) TP4 (375, 0, 8).
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4. Results and discussion 4.1. Thermal results Fig. 5 presents the contour plots of temperature results of the Lagrangian thermal model and the Eulerian thermal model, respectively. Both models produced similar heating and cooling cycles. The thermal models were verified by comparing the temperature history results from the four thermocouples positions on the base plate shown in Fig. 2a. These results are presented in Fig. 6 for the four layer specimen. As the steady-state model does not have a time related history, the thermal cycle of the testing point is obtained by plotting the temperature along lines with fixed y, and z coordinates which correspond to the thermocouple positions shown in Fig. 2a. The time coordinate is found by dividing the position in the x direction by the travel speed. Both, the transient and steady-state thermal models give accurate predictions of the temperatures at the four thermocouple positions. Although the steady state model underestimates the temperature marginally because heat can be conducted via the elements behind the heat source, the effect is small because of the high travel speed. 4.2. Mechanical results Fig. 7a and b illustrates the predicted longitudinal residual stress of the four layer wall with clamping from the two model types, which indicate similar results. The heat from the welding process causes a tensile residual stress along the weld bead due to material contraction during solidification, which causes a balancing compressive residual stress in the base plate. Note that the magnitude of the compressive stress is greatest where clamping has been applied due to the restraint in this region. There is sig-
nificant distortion of the component and relaxation of the stresses after the clamping was removed which is illustrated in Fig. 7c. To better understand these stress changes, the longitudinal stress was plotted along the dotted lines in Fig. 7b and c in Fig. 7d. Fig. 7d shows that when the specimen is clamped, the highest longitudinal stress occurs in the deposited wall. The stress predicted across the deposit is very uniform with very little annealing of the earlier layers by the latter ones. To further investigate this finding, a further four layers were deposited (giving eight layers in total) and the results plotted in Fig. 7d. There is little change in the stresses generated, further supporting this finding. Indeed Chin et al. [8] found a similar result in their model of additive layer manufacture. The stresses in the base plate adjacent to the deposited wall are also tensile, however there is a significant drop in magnitude since the material in the base is softer than the weld metal. Note that in the model there is a distinct jump in material properties at the interface which does occur in practice due to dilution effects. It is only near the bottom of the base plate that the longitudinal stresses go into compression. The significant drop in the longitudinal stress after unclamping is also shown in Fig. 7d. The interesting aspects of this plot occur toward the extremities. For example, the stress at the top of the deposited wall has a much lower value than at the interface due to the bending distortion of the sample. This distortion also causes the compressive stress at the bottom of the base plate to go into tension. There is a small reduction in the tensile longitudinal residual stress measured in the base plate with increased layers due to the influence of bending distortion. This is reflected in the residual stress measurements shown in Fig. 7d where four and eight layer walls are compared unclamped. To have an overall check of the mechanical results from the model, the predicted distortion along the long edge from the two mechanical models was compared with the measured distortion
Fig. 7. Longitudinal residual stress predictions from: (a) transient thermal and mechanical models, (b) steady state thermal and mapped mechanical models, (c) steady state thermal and mapped mechanical models after clamps were removed (a scaling factor of 5 is used for the distorted shape), and (d) the stress plotted along the lines shown in of (b and c).
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Fig. 8. Distortion verification along the longitudinal direction after the clamps were removed.
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Fig. 10. Longitudinal stress along the normal direction of the mid-section in the deposited wall.
from the two long edges of the sample. Fig. 8 shows how the distorted shape from both models is nearly identical and agrees with the experimentally measured distortion. Detailed validation of the residual stress data was provided by comparing the computational results from the one, two and three layer specimens with those from neutron diffraction measurements. Fig. 9 shows the comparison on the base plate. In both the modelling and experimental results the clamps have been removed, and three principle directions have been considered namely: longitudinal (r LD), transverse (r TD), and normal (r ND). The results are similar to those observed in long welding processes with the longitudinal stress dominating over the transverse and normal stresses [21]. The FE predictions match the experimental results well in all cases except the one layer wall where the model underpredicts the stresses. Moreover, there is a more significant reduction in the experimentally measured stresses between the 1 and 2 layer walls, than in the stresses predicted by the models. A possible explanation is that the model does not fully capture the microstructural changes which occur in the actual material. The comparison between the measured residual stresses from a 20 layer specimen with those from the model is shown in Fig. 10. In both the model and experiments the specimen is unclamped, and the comparison is along the centreline of the deposit as shown in Fig. 2b. A sample with a 20 layer wall was made to validate the residual stress on the deposited wall. Longitudinal stress was measured without clamps in the mid-section along the normal direction of the deposited wall. Due to the long computational time the transient model needed, the model based on the steady-state thermal solution was used for the prediction. The comparison shows that the numerical prediction matches the experimental result well and the overall shape is similar to that observed for the four and eight layer specimens in Fig. 7d. In general, unevenly distributed stresses generated during the WAALM process can cause large distortion of the parts after clamp removal. Depending on the application, it will be necessary to provide a subsequent heat treatment to relieve these stresses and improve the mechanical properties that would otherwise be negatively affected. The FEM models introduced in this paper can provide accurate prediction of the stresses and distortions of the WAALM process. This will be useful for future work where the WAALM process will be optimised to minimise the residual stress and distortion. 5. Conclusions Fig. 9. Stresses in the longitudinal (LD), transverse (TD) and normal (ND) directions along a transverse line in the base-plate indicated in Fig. 2a for (a) single, (b) two, and (c) three layers.
In this study, the thermo-elastic–plastic FEM is employed to simulate the thermo-mechanical performance of large multi-layer
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wall shaped WAALM structures. Experiments are carried out to verify the temperature distribution, stress distribution and distortions. Moreover, an efficient FE method based on Eulerian steadystate thermal analysis is also discussed. According to the results in this study, the following conclusions can be drawn: (1) Both FEM models can accurately predict the heating and cooling cycles during the WAALM process. The steady-state model can also be used for dealing with the multi-layer WAALM process. (2) The stress evolution analysed using the numerical model shows that stress across the deposit is very uniform with very little influence of the preceding layers on the following layers. (3) A significant stress redistribution is observed after unclamping. The stress at the top of the deposited wall has a much lower value than at the interface due to the bending distortion of the sample. The neutron diffraction strain scanner ENGIN-X reveals a good match of the predicted stress data with the measurements. The measured distortions also support the model predictions. (4) The new FEM approach based on the steady-state thermal model shows a significant advantage of around 80% on the computational time. This will be useful for future work where the WAALM process will be optimised to minimise the residual stress and distortion.
Acknowledgements This research was carried out under RUAM project (131) of the IMRC (Innovative Manufacturing Research Centre) Cranfield funded by EPSRC, UK. The authors would like to thank Flemming Nielsen for his technical assistance and Dr. Anna Paradowska for her support in ISIS.
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